ON A PERTURBED FRACTIONAL SHALLOW-WATERSYSTEM WITH CROSS OPERATORS AND DAMPINGEFFECTS

Abstract

In this paper, we study a generalized nonlinear shallow water
wave system with damping effects and cross operators involving the Khalil derivative, using regular perturbation techniques to investigate its traveling wave solutions. Applying the tanh-method, the system is reduced to a system of perturbed ordinary differential equations. By explicit substitution and algebraic manipulations, we obtain a set of compatibility conditions that govern the coefficients of the solution. A detailed case-by-case study is presented depending on the vanishing or non-vanishing of the parameters.
The results provide explicit formulas for wave profiles and derive families of solutions parameterized by wave speed c and shape parameter µ. The approach confirms that the conformable fractional derivative framework is consistent with classical shallow-water solitary waves.